This paper deals with the spallation induced by shock wave propagation in targets during the laser shock peening process. Physical aspects concerning laser-matter interaction, shock wave propagation, and spallation are considered. A continuous kinetic model for the spallation process is included in a one-dimensional finite-difference hydrodynamic code using Lagrangian coordinates in order to calculate the laser-induced spallation phenomena. Shock wave propagation in solids is calculated and validated by experimental data. The spallation zone location is then calculated for various materials with different thickness of foils and various laser shock peening parameters. The numerical simulations are compared with previously reported experimental results and good agreement is obtained for the spallation threshold and damage zone location.